The dimensional formula for pressure gradient is
- $[ML^{-1}T^{-2}]$
- $[M^1L^{-2}T^{-2}]$
- $[M^1L^2T^{-2}]$
- $[M^!L^{-1}T^{-3}]$
The Correct Option is B
Solution and Explanation
Top Questions on Dimensional Analysis
- Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length, time, and charge.
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Match List - I with List - II.
List - I List - II (A) Latent Heat (I) \( M^0 L^2 T^{-2} \) (B) Electromotive Force (II) \( M L^2 T^{-3} A^{-1} \) (C) Electrical Resistivity (III) \( M L^3 T^{-3} A^{-2} \) (D) Angular Impulse (IV) \( M L^2 T^{-1} \)
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- The coordinates of a particle with respect to origin in a given reference frame is \( (1, 1, 1) \) meters. If a force of \( \mathbf{F} = \hat{i} - \hat{j} + \hat{k} \) acts on the particle, then the magnitude of torque (with respect to origin) in \( z \)-direction is:
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- Acceleration due to gravity on the surface of earth is \( g \). If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \_\_\_\_ g.
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- In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of \( [M^a L^b T^c] \). If \( b = 3 \), the value of \( c \) is:
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Notes on Dimensional Analysis
Concepts Used:
Dimensional Analysis
Dimensional Analysis is a process which helps verify any formula by the using the principle of homogeneity. Basically dimensions of each term of a dimensional equation on both sides should be the same.
Limitation of Dimensional Analysis: Dimensional analysis does not check for the correctness of value of constants in an equation.
Using Dimensional Analysis to check the correctness of the equation
Let us understand this with an example:
Suppose we don’t know the correct formula relation between speed, distance and time,
We don’t know whether
(i) Speed = Distance/Time is correct or
(ii) Speed =Time/Distance.
Now, we can use dimensional analysis to check whether this equation is correct or not.
By reducing both sides of the equation in its fundamental units form, we get
(i) [L][T]-¹ = [L] / [T] (Right)
(ii) [L][T]-¹ = [T] / [L] (Wrong)
From the above example it is evident that the dimensional formula establishes the correctness of an equation.